Math and Logic Puzzles

[StrangerCoug]

Wrong.

[Kcdaspot]

damn.

[PersonalIdiot04]

4/52*3/51, whatever that turns out to be.

EDIT: 1/221

[StrangerCoug]

That's right!

[PersonalIdiot04]

Question is coming.

[PersonalIdiot04]

OK, so here is the question:

"In a deck of Spanish playing cards (normal, except for the fact that all 8s, 9s, and 10s have been removed), how many different hands are there that do not contain any pairs, straights, or flushes?"

[StrangerCoug]

Five-card poker hands, I presume?

[PersonalIdiot04]

Yes.

[StrangerCoug]

I've got the number of different poker hands

TOTAL

, but I'm stuck working much anything else out without cheating.

[Tragedy]

Spanish Playing cards has the normal amount of 52, right?
Remove those 8s, 9s, 10s... We'd have 40 cards..
Poker cards are usually 2 so..
...Lame.

[inspiratieloos]

There are 7*4^5*5! = 860160 straights
There are 40*9*8*7*6 = 120960 flushes
There are 7*4*5! = 3360 straight flushes

There are 40*36*32*28*24 = 30965760 hands without pairs
Hands without straights pairs or flushes = 30965760-(860160 + 120960 - 3360) = 29988000 hands

Hope I didn't forget anything (or that it is some sort of word joke)

[StrangerCoug]

I can tell that's wide of the mark since you have an eight-digit answer and drawing five from the full 52 only allows for a little under 2,600,000 hands...

[inspiratieloos]

How did you get that number?
52*51*50*49*48 = 311875200 ~ 3*10^8

[StrangerCoug]

Doing it that way makes the order of the cards in the hand matter, which they don't in poker. 10S JS QS KS AS is the same as AS KS QS JS 10S, which is the same as QS AS JS 9S KS. You want combinations, not permutations.

[inspiratieloos]

*facepalm*
So... anyone want to divide my answer by 5! ?

[StrangerCoug]

29,988,000 / 5 = 5,997,600 > 2,600,000, so 5,997,600 can't be the answer either.

[StrangerCoug]

Just for clarification, PersonalIdiot4: Threes and fours of a kind and full houses count as multiple pairs, yes?

[inspiratieloos]

5! = 1*2*3*4*5
29988000/5! = 249900

[Empking]

249900?

[inspiratieloos]

lol, now just hope that I was actually right

[PersonalIdiot04]

Both of you got it, but inspiratieloos had already guessed, so Empking gets the next question.

[Empking]

Pips easy one:
There are three countries. The land of lies (can only lie), the land of truth (can only truth) and the land of confusion (can do either). Bob says "I come from the land of lies." Where does he hail?

[KageLord]

Land of Confusion.

Here is a classic:

There are 5 rational (i.e. if something can be logically deduced, they will do so instantly) pirates: A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them.

The pirates have a strict order of seniority: A is superior to B, who is superior to C, who is superior to D, who is superior to E.

The pirate world's rules of distribution are thus: that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. If the proposed allocation is approved by a majority or a tie vote, it happens. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again.

Pirates base their decisions on three factors. First of all, each pirate wants to survive. Second, each pirate wants to maximize the number of gold coins he receives. Third, each pirate would prefer to throw another overboard, if all other results would otherwise be equal.

What will pirate A's proposal be?

[Kcdaspot]

whats the question?

[KageLord]

lol sorry. Just realized that wasn't there. Edited in.